Therapeutic and prevention clinical trials in cancer and other major diseases with mortality or irreversible morbidity are typically monitored to detect early evidence of benefit or harm, for ethical and scientific reasons. However, repeated interim analyses using conventional statistical methods will increase the likelihood of false positive claims of treatment effect. In 1983, Lan and DeMets (Biometrika) extended earlier work of Pocock, O'Brien and Fleming and others by proposing a flexible group sequential plan using an alpha spending function. However, trials terminated early may exaggerate treatment benefits or harm. We previously evaluated the degree of bias in the estimate of treatment effect and proposed bias correction estimators for the linear mixed effects model and the proportional hazards model in survival analysis. In this proposal, we continue our exploration of bias and examine a conditioned estimate of treatment effect and its properties. The condition is on the actual time of early termination. We also compare this to estimators previously evaluated by Whitehead and others. In addition, we consider the problem of allocating the total alpha level to two outcomes, one simple and the other a composite, in a sequential design. In a particular case, the simple outcome (e.g. death) is a component of the composite outcome (e.g. death plus disease recurrence or hospitalization). This issue is of particular interest to regulatory agencies where a trial is designed mainly to find a treatment effect on the composite outcome but the monitoring focuses heavily on the simple outcome. We also develop a method for dropping inferior aims in a randomized Phase II/III design, selecting the best dose for comparision based on the primary clinical outcome. For many trials such as in prevention, a best dose cannot be selected using a surrogate but requires some followup using a clinical outcome. However, following multiple arms for a clinical outcome may not be a feasible or affordable. Our proposed design allows for starting with multiple dosages, following each arm for a period of time and dropping inferior arms. Ultimately, a loading dose will be selected sequentially and composed to the control arm. This design results in efficiency in allowing patients in the leading arm to be used in the Phase III comparison and also saves time. These design issues were motivated by trials encountered in our collaboration with cancer center investigators.